134 K. YE. Veselov and V. L. Panteleyev 



fla, 271 6.28 



Let us assume that a^ ^ 10 gal, (p^ = — ,p = — = = 0.63, /^^ = 0.40. 



g Tn 10 sec 



If the distance between the axis of rotation of the Cardan suspension and the 

 axis of rotation of the pendulum does not exceed 1 cm then the last term 

 in formula (31) 



o 



is very small by comparison with a^ and can therefore be discarded. 



The periodic term a^ cos {pt-\-d^ causes the forced oscillations of the 

 system. 



This phenomenon was analysed in detail in paper (2). If we analyse equation 

 (31) we see that when horizontal accelerations are present the reading of the 

 instrument mil not correspond to the true value for gravity but to a certain 

 value of G and that we shall have to introduce the necessary corrections to 

 obtain a true reading. 



Thus we have 



4^ 2 



2 



1 



9 1 r 1 ' , f- / 2 ^1 2 2\r 9 



<Po g- +^r s+^o in ^r + 9^2 />) + j o^max g 



and further 



^x^ , ^ r^ 2 I ^Vax + 9?i ^0 / 2„ 2 , ^ 2 „2\ 

 9?o H ^ r -—((pi Til +?2 P ) 



^g 2 



(32) 



(33) 



ax" 



Here is sunply a Brown term, and the expression in square brackets 



4g 



a correction for inclination (deviation from the instantaneous vertical). 



Formula (33) can also be \^Titten 



-- = ^- 4^ + 2- [9'o + 2 + -^ \f^ ^ 17]]' 



where T/^ and Tj, are the oscillatory periods of the vessel and the Cardan 



suspension respectively. 



ax 

 For a short period Cardan suspension 992 is normally close to — , and 



o 



therefore 



aa;2 e- r a^max+n^ . 47t^Co /yi^ , ax^ 1 



^ = ^- 4^ + ^r" + — 2— + ^-U? + Fn^ 



(34) 



To assess the influence of the acceleration on an instrument mounted on 

 a Cardan suspension with natural oscillations of large period, such as a 

 stabiHzed gyroscopic device, we must return again to expression (26). 



